Credit modelling and regime-switching

Abstract

This thesis is concerned with some issues arising in relation to the capital structure and pricing of credit risk of a firm partly financed by debt. Three related models are presented. The first extends the existing literature on structural credit models of firms financed by the so called roll-over debt structure to allow for dependence between interest rates, asset volatility and the probability of default by incorporating regimes via the introduction of a Markov chain. The asset returns of a firm are modelled by a regime-switching geometric Brownian motion. An optimised capital structure is generated and the associated credit spreads analysed. The second model adds to recent work on regime-switching in the case of consol, or infinite maturity debt, by incorporating jumps into the asset process. The asset process of the firm is modelled as a phase-type Lévy process which affords a flexible framework capable of accommodating a wide range of stochastic dynamics. An optimal capital structure is identified. The contribution of the first two models is that that they are highly flexible and allow for an arbitrary number of market regimes to be combined in an intuitive way. The final model extends the literature on endogenous default to a firm which is partly financed by a single finite maturity bond. The assets of the firm are modelled as a geometric Brownian motion which pays a continuous dividend. By solving the associated optimal stopping problem, a default boundary is characterised in terms of an integral equation.